High-Threshold Low-Overhead Fault-Tolerant Classical Computation and the Replacement of Measurements with Unitary Quantum Gates

TL;DR

This paper introduces a simplified, high-threshold fault-tolerant classical computation scheme that replaces complex randomized circuits with an ordered wiring structure, enabling efficient performance calculation and practical implementation.

Contribution

It presents a novel, ordered wiring scheme that eliminates the need for randomization, reduces circuit complexity, and demonstrates a feasible method to achieve universal fault-tolerant classical computation.

Findings

Achieves a threshold close to 1/6 for fault-tolerant classical computation.

Requires only moderate code sizes, outperforming concatenation schemes.

Enables measurement-free quantum protocols with high accuracy thresholds.

Abstract

Von Neumann's classic "multiplexing" method is unique in achieving high-threshold fault-tolerant classical computation (FTCC), but has several significant barriers to implementation: i) the extremely complex circuits required by randomized connections, ii) the difficulty of calculating its performance in practical regimes of both code size and logical error rate, and iii) the (perceived) need for large code sizes. Here we present numerical results indicating that the third assertion is false, and introduce a novel scheme that eliminates the two remaining problems while retaining a threshold very close to von Neumann's ideal of 1/6. We present a simple, highly ordered wiring structure that vastly reduces the circuit complexity, demonstrates that randomization is unnecessary, and provides a feasible method to calculate the performance. This in turn allows us to show that the scheme requires only moderate code sizes, vastly outperforms concatenation schemes, and under a standard error model a unitary implementation realizes universal FTCC with an accuracy threshold of p < 5.5%, in which p is the error probability for 3-qubit gates. FTCC is a key component in realizing measurement-free protocols for quantum information processing. In view of this we use our scheme to show that all-unitary quantum circuits can reproduce any measurement-based feedback process in which the asymptotic error probabilities for the measurement and feedback are 0.51p and 1.51p, respectively.